Paper published in a journal (Scientific congresses and symposiums)
A full characterization of Bertrand numeration systems
Charlier, Emilie; Cisternino, Célia; Stipulanti, Manon
2022In Lecture Notes in Computer Science, 13257, p. 102-114
Peer reviewed
 

Files


Full Text
Charlier-Cisternino-Stipulanti-DLT2022.pdf
Author postprint (311.92 kB)
Download

All documents in ORBi are protected by a user license.

Send to



Details



Keywords :
Numeration system; Integer; Real number; Beta shift
Abstract :
[en] Among all positional numeration systems, the widely studied Bertrand numeration systems are defined by a simple criterion in terms of their numeration languages. In 1989, Bertrand-Mathis characterized them via representations in a real base β. However, the given condition turns out to be not necessary. Hence, the goal of this paper is to provide a correction of Bertrand-Mathis' result. The main difference arises when β is a Parry number, in which case two associated Bertrand numeration systems are derived. Along the way, we define a non-canonical β-shift and study its properties analogously to those of the usual canonical one.
Disciplines :
Mathematics
Author, co-author :
Charlier, Emilie  ;  Université de Liège - ULiège > Mathematics
Cisternino, Célia ;  Université de Liège - ULiège > Mathematics
Stipulanti, Manon  ;  Université de Liège - ULiège > Mathematics
Language :
English
Title :
A full characterization of Bertrand numeration systems
Publication date :
2022
Event name :
Developments in Language Theory
Event date :
du 9 mai 2022 au 13 mai 2022
Audience :
International
Journal title :
Lecture Notes in Computer Science
ISSN :
0302-9743
eISSN :
1611-3349
Publisher :
Springer, Heidelberg, Germany
Volume :
13257
Pages :
102-114
Peer reviewed :
Peer reviewed
Available on ORBi :
since 21 March 2022

Statistics


Number of views
53 (11 by ULiège)
Number of downloads
47 (7 by ULiège)

Scopus citations®
 
2
Scopus citations®
without self-citations
0
OpenCitations
 
2

Bibliography


Similar publications



Contact ORBi